Limits of the form lim _h right arrow 0 f(x + h) - f(x)/h occur frequently in calculus. Evaluate this limit for the given value of x and function f. f(x) =x^2, x=-5 The value of the limit is .

The slope of the given line d = 7t is 7 kilometers per hour. Then the correct option is A.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

Each evening, Billy jogs around the high school track at a constant rate.

The following equation describes the relationship between t, the time he jogs in hours, and d, the distance he jogs in kilometers.

d = 7t

The slope of the line will be 7,

Then graph A is correct.

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Answer:

I believe it is 24

Step-by-step explanation:

(2) (-3) (-4)

(-6) (-4)

24

Answer:

x=10,y=120

Step-by-step explanation:

3x-30=60 CDA

3x=30

x=10

again,

y+60=180 straight line

y = 120

18 will be the result of the given problem.

Applying the order of operations (PEMDAS), we first calculate the value inside the parentheses, which is 3 + 6 = 9.

Then we multiply 4 by 9, which gives 36.

Finally, we divide 36 by 2, which gives the final answer of 18. Therefore:

4 x (3 + 6) ÷ 2 = 18

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Answer:

0.4 or 2/5

Step-by-step explanation:

Dana surveyed 20 students in total and out of those 20 only 8 got an A

so:

\(\frac{8}{20}\) now if you simplify it \(\frac{4}{10}\) and if you simplify it again:

\(\frac{2}{5}\) or 0.4 in decimal

-10

Step-by-step explanation:

x = 10

x2 - 2(x + 5)

10(2) - 2(10+5)

20 - 2(15)

20 - 30

-10

Answer: 68y+106=36-y

Answer:

(-6,0)

Step-by-step explanation:

An equation of a line can be modeled as y = mx + b where m is slope and b is y-intercept.

For the line r, we can model the equation as y = mx + 3 since the line intersects y-axis at (0,3) as seen in the attachment.

For the line t, we can model the equation as y = mx - 6 as the problem gives y-intercept for line t equal to -6. Hence, the line t intersects y-axis at (0,6)

Next, we have to find the slope of line t by finding the slope of line r in the attachment. Apply the rise over run by counting the steps, you can see in the attachment that I put to learn how to count rise and run of a line. Also note that the value in attachment here is a scalar quantity, meaning only magnitude, no direction.

So we will have the slope of -1 since a line graph is heading down so the output decreases as input increases. Therefore, we know that m = -1 for both lines. Therefore, for the line t, we can model the new equation to:

\(\displaystyle{y=-x-6}\)

Then we find the x-intercept of the line by letting y = 0. Thus,

\(\displaystyle{0=-x-6}\\\\\displaystyle{x=-6}\)

Therefore, the x-intercept of line t is at (-6,0).

Answer:

(-6,0)

Step-by-step explanation:

We need to determine the equation of line r first to find the x-intercept of line t.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

\(slope = \frac{y_2 - y_1}{x_2 -x_1}\)

For line r passing through (3, 0) and (0, 3), the slope is:

\(slope = \frac{3 - 0}{0 - 3} = -1\)

Since line t has the same slope as line r, its slope is also -1.

The equation of a line in slope-intercept form (y = mx + b) is determined by its slope (m) and y-intercept (b).

We know that the slope (m) of line t is -1, and the y-intercept (b) is -6. Substituting these values into the slope-intercept form, we get:

y = -x - 6

To find the x-intercept, we set y = 0 and solve for x:

0 = -x - 6

Adding x to both sides:

x = -6

Therefore, the x-intercept of line t is (-6,0).

Answer:

It's letter b

Step-by-step explanation:

I hope this help

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.

An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.

In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.

Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.

The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.

In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.

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Answer:

64.94

Step-by-step explanation:

(49.95•30%)+49.95

Answer:

$71.36

Step-by-step explanation:

100-30=70

70÷100=0.7

49.95÷0.7=71.35715286

71.36

Answer:

E

Step-by-step explanation:

=160*250*80

=3200000cm^3

also 1000cm =1 litres

therefore 3200000cm3 =3200litres

that's all ....... have fun

Answer:

x = 7

Step-by-step explanation:

<ABC = 40 degrees.

It has 2 angles that are equal making up ABC because BD is an angle bisector.

Each of the angles = 20 degrees (1/2 of 40 = 20)

3x - 1 = 20

34 - 2x = 20

You should get the same answer if you just solve one of those equations.

3x - 1 = 20           Add 1 to both sides

3x = 20 + 1

3x = 21                Divide by 3

x = 21 / 3

x = 7

Just to make sure I'm right, we'll solve the other one.

34 - 2x = 20           Subtract 34 from both sides

-34          -34

- 2x      = - 14          Divide by -2

x = -14/-2

x = 7

There is a third way you could solve for x. You could equate the two parts

3x - 1 = 34 - 2x              Add 2x to both sides

3x+ 2x - 1 = 34              Combine

5x - 1 = 34                     Add 1 to both parts

5x = 35                          Divide by 5

5x/5 = 35/5

x = 7

Step-by-step explanation:

speed=distance÷time

A.V.S=440÷11=40m/s

hope it helps.. Please mark brainliest.

Answer:

40 m/s

Step-by-step explanation:

Find:

We are asked to find the unit rate, How many meters per 1 second?

Know:

440 meters in 11 seconds

Solve:

440 meters in 11 seconds

  ? meters in 1 second

   440/11  = 40 meters per second

Answer:

The average speed of the person is 40 m/s

Answer:

Step-by-step explanation:

Hello,

\(h(g(x))=h(3x+2)\\ \\=-5\times (3x+2)+1\\\\=-15x-10+9\\\\=-15x-1\)

Thanks

Answer:

-6, -3, 0, and 3

Step-by-step explanation:

Hope this helps.

Answer:

-2, -6

-1, -3

0, 0

1, 3

Step-by-step explanation:

Substitute the value of x in the given rule

For x = -2

y=3x

y= 3(-2)

y= -6

For x = -1

y=3x

y= 3(-1)

y= -3

For x = 0

y=3x

y= 3(0)

y= 0

For x = 1

y=3x

y= 3(1)

y= 3

Answer:

$12.25

Step-by-step explanation:

1.75 x 7 = 12.25

Answer: The answer is C

Step-by-step explanation:

1.2% is basically 0.012. 12% is 0.12 and then 1.02 and 1.2. what i'm trying to get at here is when you are working with percents, 100% is 1. so anything below that is going to be a decimal, for an example, 34% would be 0.34, and 68% would be 0.68. Also 0.18% would be 0.0018. Once you know how to convert percentages to decimals, doing those kind of questions is pretty easy.

Based on simple interest, the solution to the question is that his friend will ultimately owe Darrel $2,875.

A loan or investment's interest can be calculated using simple interest using the principal, interest rate, and duration of the transaction. Because it just considers the original principal and does not account for any compounded interest, it is known as "simple" interest.

Darrel will be indebted to his friend for the following sum if he lends him $2,500 and receives repayment with 15% simple interest after a year:

Interest = Principal x Rate x Time

Interest = $2,500 x 0.15 x 1

Interest = $375

Thus, the total sum his friend will be required to pay Darrel is:

Total amount = Principal + Interest

Total amount = $2,500 + $375

Total amount = $2,875

Thus, the total amount his friend owes Darrel is $2,875.

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Answer:

k = -17 + 4x

Step-by-step explanation:

Simplifying

4x + -1k = 17

Reorder the terms:

-1k + 4x = 17

Solving

-1k + 4x = 17

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-4x' to each side of the equation.

-1k + 4x + -4x = 17 + -4x

Combine like terms: 4x + -4x = 0

-1k + 0 = 17 + -4x

-1k = 17 + -4x

Divide each side by '-1'.

k = -17 + 4x

From both the table and the graph, it can be concluded that the points given in the table lies on the parabola y =  x²  

What is graph of a function ?

At first it is important to know about function.

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Graph of a function f(x) is the collection of points of the form (x, f(x))

x           x²                 (x, y)

-3        9                   (-3, 9)

-2        4                   (-2, 4)

-1         1                    (-1, 1)

0        0                   (0, 0)

1         1                     (1, 1)

2        4                    (2, 4)

3         9                   (3, 9)

The graph has been attached.

From both the table and the graph, it can be concluded that the points given in the table lies on the parabola y =  x². 

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The 3rd and 4th expressions cannot be simplified using the quotient rule for exponents

The quotient rule for exponents states that if you have two exponents, and you want to divide them, you can do so by subtracting the exponent of the denominator from the exponent of the numerator.

The general form of the quotient rule:

xᵃ / xᵇ = xᵃ⁻ᵇ

Given:

(3²9⁻¹2³)/(8⁵7⁻²)

(3²9⁻¹2³)/(8⁵7⁻²) = (3² × 3²⁽⁻¹⁾ × 2³)/(8⁵×7⁻²)

                        = (3² × 3⁻² × 2³)/(2³⁽⁵⁾ ×7⁻²)

                        = (3²⁺⁽⁻²⁾ × 2³)/(2¹⁵ × 7⁻²)

                        = (3⁰ × 2³)/(2¹⁵ × 7⁻²)

                        = (1 × 2³)/(2¹⁵ × 7⁻²)

                        = (2³)/(2¹⁵ × 7⁻²)

                       = 2³⁻¹⁵ × 7²    ( quotient rule is used here)

                       = (2⁻¹²) (7²)

(4⁻²x⁻¹)/(4⁻¹x⁻²)

(4⁻²x⁻¹)/(4⁻¹x⁻²) = 4⁻²⁻⁽⁻¹⁾ × x⁻¹⁻⁽⁻²⁾  ( quotient rule is used here)

                       = 4⁻²⁻⁽⁻¹⁾ × x⁻¹⁻⁽⁻²⁾

                       = (4⁻¹) (x¹)

(6x⁻⁸z²)(6⁵x⁻¹z²)

(quotient rule cannot be used to simplify this expression because the two expressions are multiplying each other)

(q⁻⁵r¹¹)/(s⁶t⁻¹⁵)

(quotient rule cannot be used here  because there are no like bases)

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The angle in degrees is 873.1843.

Let the measure of the angle be θ in degrees. Therefore, the measure of the same angle in gradians is (θ × π/180).

According to the given information, the number of degrees of a certain angle added to the number of gradians of the same angle is 152.(θ) + (θ × π/180) = 152.

Simplifying the above equation, we get:(θ) + (θ/180 × π) = 152.

Multiplying both sides of the equation by 180/π, we get:

θ + θ = (152 × 180)/π2θ = (152 × 180)/πθ = (152 × 180)/(3.14)θ = 873.1843

Thus, the angle in degrees is 873.1843.

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True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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The value x in the secant line using the Intersecting theorem is 4.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

First sectant line segment = ( x - 1 ) + 5

External line segment of the first secant line = 5

Second sectant line segment = ( x + 2 ) + 4

External line segment of the second secant line = 4

Using the Intersecting secants theorem:

5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )

Solve for x:

5( x - 1 + 5 ) = 4( x + 2 + 4 )

5( x + 4 ) = 4( x + 6 )

5x + 20 = 4x + 24

5x - 4x = 24 - 20

x = 4

Therefore, the value of x is 4.

Option C) 4 is the correct answer.

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Answer:

$633

Step-by-step explanation:

Overtime:

(41 - 35 + 39 - 35) hours = 10 hours

Overtime rate: ($7.70 + $1.70)/hour = $9.40/hour

Regular time:

(35 + 35) hours = 70 hours

Regular rate: $7.70/hour

total pay = regular pay + overtime pay

total pay = $7.70/hour × 70 hours + $9.40/hour × 10 hours

total pay = $633

Answer:

2.5

Step-by-step explanation:

the other persons answer is wrong

The number after rounding to the one significant figure is 4000.

The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation

Rounding off means a number is made simpler by keeping its value intact but closer to the next number

According to the given question we have an expression.

\(\frac{798}{8} (41)\)

When we evaluate this expression we get

\(\frac{798}{8} (41)\)

\(=99.75(41)\)

\(= 4089.75\)

Here, the first significant figure is 4 and the second one is 0 which is less than 5.

Hence, the number after rounding to the one significant figure is 4000.

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Answer:

Base = 10 ft. and the height = 6.

Step-by-step explanation:

Area of triangle = 1/2bh

base is 4 + h  ⇔  base = 4 + h

height = h

Using the formula for the area of triangle substitute into the formula the given facts.

A = 1/2bh

30 = 1/2(4 + h) (h)

30 = 1/2(4h + h²)     Multiply both sides by 2

60 = 4h + h²

-60 =           -60      Add -60 to both sides

0 = h²+ 4h -60        

(h + 10)(h - 6) = 0      Factor

h + 10 = 0    h - 6 =0

h = -10         h = 6

reject any negative number and use the positive answer for h.

So h = 6      and the base = 4 + 6 ; base = 10

Answer:

approximately 28.26 square feet

Step-by-step explanation:

The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.

The area is:

28.27 square feet

Work/explanation:

Since the tabletop is circular, we use the formula for a circle's area, which is: \(\bf{A=\pi r^2}\).

We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.

Now, here's a diagram for you;

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}\)

Plug in the data:

\(\sf{A=\pi\times3^2}\)

\(\sf{A=\pi\times9}\)

\(\sf{A=28.27\:ft^2}\)